It came into being in 1970 under the Synodical Government Measure 1969, replacing a body called the Church Assembly.
Its membership comprises three Houses:
The House of Bishops comprising all the Diocesan Bishops, a small number of Suffragan Bishops who are elected and a few others;
The House of Clergy which, as its origins date back to medieval times, often operates as the Convocation of Canterbury or York (Liverpool is in York!). It consists principally of clergy elected from Dioceses in relation to the number of clergy plus others appointed by the Forces, Religious Orders, and Universities, etc;
The House of Laity which comprises mainly representatives from Dioceses elected according to the total electoral roll. There are other members from the Forces, ex officio, etc.
The Synod normally meets twice a year – February in London and July in York and, when the business demands it, in November (also in London).
Quoting from the national Church of England website which has lots of useful background.
It has powers in the following areas:
Legislation by Measure
To pass Measures which, if approved by resolution of each House of Parliament, receive Royal Assent and thereby become part of the law of England
Legislation by Canon
To legislate by Canon, subject to Royal Licence and Assent
Relations with other Churches
To regulate the Church of England’s relations with other churches and to make provisions for matters relating to worship and doctrine. It can make provision by Act of Synod, regulation or other instrument in cases where legislation by or under a Measure or Canon is not necessary
Liturgy and Doctrinal Assent
To approve, amend, continue or discontinue liturgies and make provision for any matter (except the publication of banns of marriage) to which rubrics of the Book of Common Prayer relate and to ensure that the forms of service contained in the Book of Common Prayer continue to be available for use in the Church of England. The Synod also decides the form in which ministers and officers of the Church of England are required to assent to the doctrine of the Church of England (the Declaration of Assent).
To consider any other matters of religious or public interest
To approve (or reject) the central church budget each year.